The saturation number of induced subposets of the Boolean lattice.

Given a poset P, a family F of elements in the Boolean lattice is said to be P-saturated if (1) F contains no copy of P as a subposet and (2) every proper superset of F contains a copy of P as a subposet. The maximum size of a P-saturated family is denoted by La(n,P), which has been studied for a number of choices of P. The minimum size of a P-saturated family, sat(n,P), was introduced by Gerbner et al. (2013), and parallels the deep literature on the saturation function for graphs.